Overview
- Group
- SmallGroup(360,154)
- Rank
- 3
- Schläfli Type
- {30,6}
- Vertices, edges, …
- 30, 90, 6
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
9-fold
10-fold
15-fold
18-fold
30-fold
45-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(16,31)(17,35)(18,34)(19,33)(20,32)(21,41)(22,45)(23,44)(24,43)(25,42)(26,36)(27,40)(28,39)(29,38)(30,37)(47,50)(48,49)(51,56)(52,60)(53,59)(54,58)(55,57)(61,76)(62,80)(63,79)(64,78)(65,77)(66,86)(67,90)(68,89)(69,88)(70,87)(71,81)(72,85)(73,84)(74,83)(75,82);; s1 := ( 1,67)( 2,66)( 3,70)( 4,69)( 5,68)( 6,62)( 7,61)( 8,65)( 9,64)(10,63)(11,72)(12,71)(13,75)(14,74)(15,73)(16,52)(17,51)(18,55)(19,54)(20,53)(21,47)(22,46)(23,50)(24,49)(25,48)(26,57)(27,56)(28,60)(29,59)(30,58)(31,82)(32,81)(33,85)(34,84)(35,83)(36,77)(37,76)(38,80)(39,79)(40,78)(41,87)(42,86)(43,90)(44,89)(45,88);; s2 := (16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(90)!( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(16,31)(17,35)(18,34)(19,33)(20,32)(21,41)(22,45)(23,44)(24,43)(25,42)(26,36)(27,40)(28,39)(29,38)(30,37)(47,50)(48,49)(51,56)(52,60)(53,59)(54,58)(55,57)(61,76)(62,80)(63,79)(64,78)(65,77)(66,86)(67,90)(68,89)(69,88)(70,87)(71,81)(72,85)(73,84)(74,83)(75,82); s1 := Sym(90)!( 1,67)( 2,66)( 3,70)( 4,69)( 5,68)( 6,62)( 7,61)( 8,65)( 9,64)(10,63)(11,72)(12,71)(13,75)(14,74)(15,73)(16,52)(17,51)(18,55)(19,54)(20,53)(21,47)(22,46)(23,50)(24,49)(25,48)(26,57)(27,56)(28,60)(29,59)(30,58)(31,82)(32,81)(33,85)(34,84)(35,83)(36,77)(37,76)(38,80)(39,79)(40,78)(41,87)(42,86)(43,90)(44,89)(45,88); s2 := Sym(90)!(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90); poly := sub<Sym(90)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.